Data Driven Density Functional Theory: A case for Physics Informed Learning

Classical DFT offers an incredibly versatile and user-friendly framework for modelling many-body systems. Yet, its potential for widespread adoption across a variety of fields, including biology, nanofluidics, chemical engineering -- to name but a few -- is held back by the simple fact that accurate free energy functionals are known only for a handful of rather special systems. Present work is, to our knowledge, a first attempt to develop an algorithmic data-driven inference method for classical DFT functionals, equipped with full uncertainty quantification. Present work offers a first step towards inferential modelling of many-body systems, where small-scale simulations are used to algorithmically capture essential patterns of their collective behaviour. Thus, yielding an analytic description that can be scaled to system sizes beyond simulation capabilities.